a message from a lady friend; suppose the lady went to see him accompanied by a friend whom Sir Horace did not like—­a friend of whom Sir Horace was jealous.  Suppose they asked for money—­blackmail—­and there was a quarrel in which Sir Horace was shot.  Then we have your idea as to how the lady’s handkerchief was torn—­I agree with that in the main.  The lady and her friend fled from the place.  Later in the night the place is burgled by some one who has had his eye on it for some time, and on entering the library he is astounded to find the dead body of the owner.  Suppose he went home, and on thinking things over sent the letter to Scotland Yard with the idea that if the police got on to his tracks about the burglary the fact that he had told us about the murder would show he had nothing to do with killing Sir Horace.”

“That is a good theory, too,” said Rolfe, in a meditative tone.  “And the only person who can tell us which is the right one is Sir Horace’s lady friend.  The problem is to find her.”

“Right,” said the inspector approvingly.  “And while you have been making inquiries at the shops about the handkerchief I have been down to the Law Courts branch of the Equity Bank where Sir Horace kept his account.  It occurred to me that a look at Sir Horace’s account might help us.  You know the sort of man he was—­you know his weakness for the ladies.  But he was careful.  I looked through his private papers out at Riversbrook expecting to get on the track of something that would show some one had been trying to blackmail him over an entanglement with a woman, but I found nothing.  I couldn’t even find any feminine correspondence.  If Sir Horace was in the habit of getting letters from ladies he was also in the habit of destroying them.  No doubt he adopted that precaution when his wife was alive, and found it such a wise one that he kept it up when there was less need for it.  But a weakness for the ladies costs money, Rolfe, as you know, and that is why I had a look at his banking account.  He made some payments that it would be worth while to trace—­payments to West End drapers and that sort of thing.  Of course, Sir Horace, being a cautious man and occupying a public position, might not care to flaunt his weakness in the eyes of West End shopkeepers, and instead of paying the accounts of his lady friend of the moment, may have given her the money and trusted to her paying the bills—­a thing that women of that kind are never in a hurry to do.  In that case the payments to West End shopkeepers are for goods supplied to his daughter.  However, I’ve taken a note of the names, dates, and amounts of a number of them, and I want you to see the managers of these shops.”

“We are getting close to it now,” said Rolfe, approvingly.